Gonzalez-Sanchez, Jon and Klopsch, Benjamin (2011) On w-maximal groups. Journal of Algebra, 328
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Let $w = w(x_1,..., x_n)$ be a word, i.e. an element of the free group $F = $ on $n$ generators $x_1,..., x_n$. The verbal subgroup $w(G)$ of a group $G$ is the subgroup generated by the set $\{w (g_1,...,g_n)^{\pm 1} | g_i \in G, 1\leq i\leq n \}$ of all $w$-values in $G$. We say that a (finite) group $G$ is $w$-maximal if $|G:w(G)|> |H:w(H)|$ for all proper subgroups $H$ of $G$ and that $G$ is hereditarily $w$-maximal if every subgroup of $G$ is $w$-maximal. In this text we study $w$-maximal and hereditarily $w$-maximal (finite) groups.
This is a Submitted version This version's date is: 15/2/2011 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/29ac0f41-96a9-643b-cca9-4cbe396cf682/7/
Deposited by Research Information System (atira) on 18-Nov-2014 in Royal Holloway Research Online.Last modified on 18-Nov-2014
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